Let f:[1,∞] be a differentiable function such that f(1)=2. If 6∫1xf(t)dt=3xf(x)−x3 for all x≥1, then the value of f(2) is
Form the differential equation of the family of hyperbola having foci on x-axis and center at the origin.
The general solution of a differential equation of the type dydx+P1x=Q1is(A) ye∫P1dy=∫(Q1e∫P1dy)dy+C (B) ye˙∫P1dx=∫(Q1e∫P1dx)dx+C(C) xe∫P1dy=∫(Q1e∫P1dy)dy+C (D) xe∫p1dx=∫Q1e∫p1dxdx+C
Find the equation of a curve passing through the point (0, 1). If the slope of the tangent to the curve at any point (x, y) is equal to the sum of the x coordinate (abscissa) and the product of the x coordinate and y coordinate (ordinate) of that point.
In a bank, principal increases continuously at the rate of 5% per year. An amountof Rs 1000 is deposited with this bank, how much will it worth after 10 years(e0.5=1.648)
The number of arbitrary constants in the general solution of a differential equationof fourth order are:(A) 0 (B) 2 (C) 3 (D) 4